Biology Reference
In-Depth Information
FIGURE 11.8 Kaplan e Meier
plot ( Kaplan and Meier, 1958 )of
the survivorship from 250 simu-
lated ages-at-death (solid line
step function) and the 95%
confidence intervals for survi-
vorship estimated from the
simulated femur length data
(dashed smooth curves).
Simulation of 250 Immature Deaths
0
2
4
6
8
10
12
14
Age
these reasons, it is important to assess the goodness of fit between functions empirically
generated from observed skeletal data and those from the fitted model. As an example,
consider the goodness of fit between the empirical cumulative density for the femur lengths
(that we simulated) and the cumulative density that our estimated parameter(s) in the hazard
model implies. The empirical cumulative density function is just a step function that rises by
1/n at each value of, in this case, sorted femoral length. From Equation 11.17 we can write the
modeled cumulative density function (cdf) for femoral length as
Z FL
cdf ðFLÞ¼
f ðxjlÞ:
(11.19)
x¼0
Figure 11.9 shows the empirical cumulative density function and the modeled one from
Equation 11.19 . The fit appears quite good in this example for the same reasons as in the
preceding paragraph.
Estimating the Ages-at-Death
As with estimating the sex of individuals following estimation of the sex ratio, we often
want to estimate individual ages-at-death after estimating the age-at-death structure. We first
approach this as a problem in point age estimation, where we want to estimate the most likely
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